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Mimetic finite differences for elliptic problems

Franco Brezzi, Annalisa Buffa, Konstantin Lipnikov (2009)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

We developed a mimetic finite difference method for solving elliptic equations with tensor coefficients on polyhedral meshes. The first-order convergence estimates in a mesh-dependent H 1 norm are derived.

Mimetic finite differences for elliptic problems

Franco Brezzi, Annalisa Buffa, Konstantin Lipnikov (2008)

ESAIM: Mathematical Modelling and Numerical Analysis

We developed a mimetic finite difference method for solving elliptic equations with tensor coefficients on polyhedral meshes. The first-order convergence estimates in a mesh-dependent H1 norm are derived.

Minimal Graphs in ℍ n × ℝ and ℝ n + 1

Ricardo Sà Earp, Eric Toubiana (2010)

Annales de l’institut Fourier

We construct geometric barriers for minimal graphs in ℍ n × ℝ . We prove the existence and uniqueness of a solution of the vertical minimal equation in the interior of a convex polyhedron in ℍ n extending continuously to the interior of each face, taking infinite boundary data on one face and zero boundary value data on the other faces.In ℍ n × ℝ , we solve the Dirichlet problem for the vertical minimal equation in a C 0 convex domain Ω ⊂ ℍ n taking arbitrarily continuous finite boundary and asymptotic boundary data.We prove...

Minimal surfaces in pseudohermitian geometry

Jih-Hsin Cheng, Jenn-Fang Hwang, Andrea Malchiodi, Paul Yang (2005)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

We consider surfaces immersed in three-dimensional pseudohermitian manifolds. We define the notion of (p-)mean curvature and of the associated (p-)minimal surfaces, extending some concepts previously given for the (flat) Heisenberg group. We interpret the p-mean curvature not only as the tangential sublaplacian of a defining function, but also as the curvature of a characteristic curve, and as a quantity in terms of calibration geometry. As a differential equation, the p-minimal surface equation...

Minimal tori in S4.

U. Pinkall, D. Ferus, I. Sterling (1992)

Journal für die reine und angewandte Mathematik

Minimising convex combinations of low eigenvalues

Mette Iversen, Dario Mazzoleni (2014)

ESAIM: Control, Optimisation and Calculus of Variations

We consider the variational problem         inf{αλ1(Ω) + βλ2(Ω) + (1 − α − β)λ3(Ω) | Ω open in ℝn, |Ω| ≤ 1}, for α, β ∈ [0, 1], α + β ≤ 1, where λk(Ω) is the kth eigenvalue of the Dirichlet Laplacian acting in L2(Ω) and |Ω| is the Lebesgue measure of Ω. We investigate for which values of α, β every minimiser is connected.

Minoration du spectre des variétés hyperboliques de dimension 3

Pierre Jammes (2012)

Bulletin de la Société Mathématique de France

Soit M une variété hyperbolique compacte de dimension 3, de diamètre  d et de volume ≤ V . Si on note μ i ( M ) la i -ième valeur propre du laplacien de Hodge-de Rham agissant sur les 1-formes coexactes de M , on montre que μ 1 ( M ) ≥ c d 3 e 2 k d et μ k + 1 ( M ) ≥ c d 2 , où c > 0 est une constante ne dépendant que de V , et k est le nombre de composantes connexes de la partie mince de M . En outre, on montre que pour toute 3-variété hyperbolique M ∞ de volume fini avec cusps, il existe une suite M i de remplissages compacts de M ∞ , de diamètre d i → + ∞ telle que et μ 1 ( M i ) ≥ c d i 2 .

Currently displaying 221 – 240 of 517